Any interesting properties of $\sqrt{\sqrt{100x+1}-1}=y$

Question

Are there any interesting properties of: $$\sqrt{\sqrt{100x+1}-1}=y$$ Where $x$ and $y $ are non-negative real intergers. I'm thinking about what is the digit root? Are there any interesting quirks on divisibility? Or alternatively (may not be found from previous equation) $$\sqrt{100x+1}=100a+1$$

Answer 1

Upon squaring both sides we come up with $$ 100x=y^4 + 2y^2$$

Some integral solutions are found by $y=10k$ and $x= 100k^4+2k^2$ for integer values of $k$.

For example for $k=1$, we get $x=102$ and $y=10$